Counter
5.5 Low-Noise Microwave Generation via Optical Frequency DivisionDivision
frequency combs and electronic division [135]. The current stability can be improved fur- ther by making the spiral resonator with longer optical roundtrip length and thicker silica layer, which will result larger optical mode volume. The density of device (roundtrip length per unit area) can be also enhanced by adopting silica ridge structure. SiN-waveguide inte- grated structure is also possible[89] and it allows the spiral resonator to be integrated with other chip-based optical components. Particularly, this on-chip frequency reference can be combined with microcomb technology[39, 40, 41] to provide broad-bandwidth synthesis of low-phase-noise signals from RF to optical domain. In addition, the high optical coherence from on-chip reference cavity can enhance the performance of many chip-based systems in the field of communication[136], remote sensing [137], atomic physics [94, 138], and spectroscopy[85]. Its scalable and integrable nature combined with the performance re- ported here makes the spiral resonator an appealing on-chip reference cavity for portable optical devices.
5.5 Low-Noise Microwave Generation via Optical Frequency
same theoretical limit with the approach using one optical reference (or 1-point lock OFD), 2-point lock OFD is suitable for portable systems because the common noise cancellation gives immunity to external vibration/acoustic noise and it does not need the complex self- referencing of frequency comb[145]. An electro-optical method is also demonstrated for the 2-point lock OFD. In this method, optical frequency combs are generated through a cascade of direct phase modulation and self-phase modulation of the two optical frequen- cies by using a voltage controlled electrical oscillator[152]. This electro-optical frequency division (EOFD) method is simple relative to other comb generation methods. It is also tun- able and scalable to higher division ratios within the tunable range of the voltage controlled oscillator and the phase modulator.
In this section, stable microwave is generated from two laser lines locked to the on-chip spiral reference cavity via EOFD method.
Figure 5.9(a-b) illustrates the measurement setup. Two fiber lasers with two different frequencies were combined by a bi-directional coupler and evanescently coupled to the spiral resonator via tapered fiber. The spiral resonator has the round-trip length of 1.2 meter, equivalent to the free-spectral-range of 167 MHz. The typical quality factor of the device is 50 ∼ 100 million. The coupled optical power is approximately 3 mW for each laser. The two fiber lasers are independently locked to the optical modes of the spiral resonator using Pound-Drever-Hall system (Figure 5.9(a)).
Then, the two frequency-stabilized lasers are tapped and combined through 50/50 fiber- coupler. The combined laser lights are introduced into the electro-optical frequency divider[153]
as shown in figure 5.9(b), which generates frequency combs around the two stabilized laser frequencies with the spectral line spacing set by the voltage-controlled electrical oscil- lator(VCO). Optical spectra of the two frequency-stabilized laser lines and cascaded side- bands are recorded using Yokogawa AQ6370D optical spectrum analyzer (OSA). The over- lapping comblines at the midpoint are optically filtered and photodetected. The detected beatnote signal is phase-locked to the∼10 MHz offset frequency from an oven-controlled crystal oscillator (OCXO) by a feedback control. The phase noise spectrum and electrical spectrum of the phase-locked VCO signal are measured using Rohde Schwartz FSUP26.
Fractional frequency instability is also measured using the Tektronix FCA3120 frequency
Spiral Resonator PC
PDH Locking Loop 1
PDH Locking Loop 2 Fiber Laser
fopt1
PID
PID PC
PC
PC
PD Mixer
EOM
MIxer LO ~
EOM LO
PD
Electrical signal Optical signal Fiber Laser
fopt2
FRRs Q ~ 50 M
Q ~ 50 M
Q ~ 500 M
a
fopt1
fopt2
~
Frequency
Power
b
fopt1 fopt2
OBPF
fvco
PD
~ VCO
EOM OSA
L(f) Analyzer / ESA
fvco
Frequency Counter
EDFA
HNLF
PID
Feedback Loop
~
OCXO
Figure 5.9:Experimental setup for optical frequency division using a spiral refer- ence cavity.(a) Setup for generation of relatively stable two laser lines locked to the spiral resonator. Two fiber lasers with two different frequencies (fopt1andfopt2) were combined and evanescently coupled to the spiral resonator via tapered fiber. The po- larization controllers (PC) are used to change the polarization of lasers. The two fiber lasers are independently phase-locked to the optical modes of the spiral resonator us- ing Pound-Drever-Hall (PDH) feedback loop. Instead of the spiral resonator, two fiber ring resonators (FRRs) with different quality(Q)-factors (50 million and 500 million) are also used. Then, the two frequency-stabilized lasers are tapped and combined through a 50/50 fiber-coupler. (b) A schematic of the electro-optical frequency divider to generate a microwave signal. The combined two stabilized laser lines are introduced to the electro- optic modulator (EOM) and phase modulated to generate cascaded sidebands around each laser line. The frequency spacing between the sidebands are determined by the frequency of voltage controlled oscillator (VCO). The cascaded sidebands are spectrally broadened to generate two overlapping combs after passing erbium-doped fiber amplifier (EDFA) and highly nonlinear fiber (HNLF). The two overlapping comblines at the mid point are optically filtered and photodetected to generate∼10 MHz beat frequency. The beat fre- quency is phase-locked to the oven-controlled crystal oscillator (OCXO) via feedback loop. The phase noise spectra, L(f), and RF power spectra of the two combline beat fre- quency and the VCO frequency(fV CO) are measured using phase noise analyzer / elec- trical spectrum analyzer (ESA). Fractional frequency instability of the VCO frequency is also measured using a frequency counter. The optical spectrum is measured using an optical spectrum analyzer (OSA). PD : Photo Detector, LO : Local Oscillator, PID : Pro- portional - Integral - Derivative controller.
counter.
As a first step, the reference phase noise before frequency division is studied by mea- suring the phase noise of 167 MHz beatnote from two stabilized fiber lasers near 1550 nm which are locked to two adjacent modes of same mode-family in the spiral resonator (Figure 5.10). Within the 200 kHz current modulation bandwidth of the fiber lasers, the phase noise (red curve) has improved significantly and 15 dBc/Hz is measured at 1 Hz offset frequency, which is more than 60 dB lower than the phase noise measured from the two free-running fiber lasers (black curve). The theoretical thermo-refractive noise of the 1.2-meter spiral resonator at 167 MHz carrier frequency,
L167 MHz(f) =
167 MHz 193.5 THz
2
×L193.5 THz(f), (5.6)
is also plotted (cyan dashed line). Here, L193.5 THz(f) is the theoretical one-sided phase noise of the spiral resonator at 193.5 THz optical carrier frequency, which sets the fun- damental noise limit of the spiral resonator and is already derived in section 5.4. The measured phase noise is much higher than the theoretical thermo-refractive noise limit and this discrepancy originates from low signal-to-noise of frequency discriminator signal in the PDH feedback loop, which results in not enough servo gain to suppress the intrinsic laser noise[154]. To confirm this, we repeated the same phase noise measurement using 2-meter-long fiber ring resonators (FRRs) with two different Q-factors, 50 million (green curve) and 500 million (blue curve), having the same free-spectral range (FSR) of 100 MHz. While the FRR with Q∼50 million shows similar phase noise level with the spiral resonator, the FRR with Q∼500 million shows∼20 dB lower phase noise. This confirms that the measured phase noise of the spiral resonator is limited by the low signal-to-noise in the PDH feedback loop and can be further improved by increasing the Q-factor of the spiral resonator.
As a next step, two fiber lasers at 1549.9 nm and 1564.6 nm are phase-locked to the spiral resonator and two relatively stable optical frequencies having 1.817 THz difference frequency are generated. As shown in figure 5.11(a), frequency combs (cascaded sidebands of the two stable optical lines) are created through electro-optic modulation and spectrally
Offset Frequency (Hz)
100 101 102 103 104 105 106 107
L(f) (dBc/Hz)
-140 -120 -100 -80 -60 -40 -20 0 20 40 60 80 100
free-running fiber lasers
1.2 m spiral resonator (Q ~ 50 M) 2 m fiber ring resonator (Q ~ 50 M) 2 m fiber ring resonator (Q ~ 500 M) theoretical noise limit @ 167 MHz
Figure 5.10:Phase noise spectra of the heterodyned two fiber lasers near 1550 nm.
One-sided phase noise spectra of the beatnotes from two free-running fiber lasers (black curve) and two fiber lasers phase-locked to the 1.2 m spiral resonator (red curve). The beat frequency is 167 MHz, which is the free spectral range (FSR) of the spiral resonator, and the frequencies of two fiber lasers are around 1550 nm. The phase noise is reduced within the 200 kHz current modulation bandwidth of fiber lasers and the reduction factors are 60 dB below 100 Hz and 40 dB at 1 kHz offset frequency. The improved phase noise is 100 dB higher than the theoretical thermorefractive noise (cyan dashed line) at 167 MHz carrier frequency and limited by the low signal-to-noise in the Pound-Drever-Hall (PDH) feedback loop. The phase noise spectra measured from two fiber ring resonators with different quality factors, 50 million (green curve) and 500 million (blue curve), show that the phase noise can be further reduced by improving the quality factor of the spiral resonator.
Wavelength (nm)
1540 1545 1550 1555 1560 1565 1570 1575
dBm
-80 -60 -40 -20 0 a
Offset Frequency (Hz)
100 101 102 103 104 105 106 107
L(f) (dBc/Hz)
-140 -120 -100 -80 -60 -40 -20 0 b
Frequency (11.98GHz + kHz)
-2 0 2
dBm
-100 -50 0 c
τ [sec]
10-2 10-1 100 101 σy(τ)
10-9 10-8 10-7 d
-160 -180 20 40
after division by 152 theoretical noise limit FSUP26 detection limit before division
RBW = 20 Hz
Figure 5.11:Stable microwave generation via optical frequency division. (a) Optical spectra of two pump lasers (black), narrow combs around pump lasers after the cascaded phase modulation (blue) and overlapped combs after spectral broadening (red). The two pump laser lines are 1.817 THz apart and the frequency of the voltage controlled oscil- lator (VCO) is 11.97 GHz. (b) One-sided phase noise spectra measured before and after optical frequency division (OFD) are shown. Before frequency division, phase noise is measured from 9.5 MHz beat frequency of the optically filtered comblines at the over- lapped region (blue curve). After frequency division, phase noise is measured from the phase-locked VCO signal at 11.97 GHz (red curve). Average phase noise reduction is
∼44dB which is the division factor (1.817 THz / 11.97 GHz = 152) squared . The theo- retical thermorefractive noise at 11.97 GHz carrier frequency (cyan dashed line) and the detection limit of the phase noise analyzer, Rohde Schwarz FSUP26,(black dotted line) are also shown. (c) Electrical power spectrum of the phase-locked VCO signal within 6 kHz span. Resolution bandwidth (RBW) is 20 Hz. (d) Fractional frequency instability, σy(τ), over the averaging time (τ) from 3 ms to 10 s.
broadened to overlap at the mid point. The overlapping comblines are filtered by using a fiber-bragg-grating optical filter and the phase noise spectrum of∼10 MHz beat frequency is measured as a reference phase noise level before frequency division (blue curve in figure 5.11(b)). The reference phase noise spectrum includes the phase noise of VCO (Agilent PSG microwave synthesizer) magnified by optical division factor (1.817 THz / 11.97 GHz
= 152) in addition to the phase noise of 1.817 THz beatnote. Above 1 kHz offset frequency, the phase noise is limited by the magnified VCO noise.
After electro-optical frequency division by phase-locking the two combline beat fre- quency to OCXO offset frequency (∼ 10 MHz), the phase noise spectrum of the phase- locked VCO frequency (∼ 11.97 GHz) is measured (red curve in figure 5.11(b)). On average, it has improved from the reference level by 44 dB, which is the division factor squared (152×152 = 23104∼44 dB ). However, it is>30dB higher than the theoretical thermorefractive noise (cyan dashed line in figure 5.11(b)). Again, it is limited by the un- suppressed intrinsic laser noise due to the low signal-to-noise in the PDH feedback loop.
The servo-conrol bump is also shown near 200 kHz, limiting the phase noise around the offset frequency.
Figure 5.11(c) shows the electrical power spectrum of the stabilized 11.97 GHz VCO signal within 6 kHz span. The resolution bandwidth is 20 Hz. Fractional frequency in- stabilities are also measured at the averaging times from 3 ms to 10 s, and minimum of 1.68×10−9 is measured at 0.7 s (Figure 5.11(d)). It’s worth noting that there’s no vacuum system or temperature stabilization to achieve this value. Although the measured stability is limited by the technical noise of the PDH feedback loop, the theoretical noise limit can be reached by enhancing the Q-factor of the spiral resonator. Current Q-factor is limited by the surface scattering loss of the spiral resonator and can be improved by the optimization of device fabrication process. Alternative way to achieve the theoretical limit is increasing the division factor using two laser lines with a larger frequency difference. Ideally, 30-fold improvement of the quality factor (from 50 million to 1.5 billion) or the division factor (from 1.817 THz to 60 THz) will be needed to reach the theoretical limit and this will reduce the fractional frequency instability by 15 dB.
Furthermore, we can also reduce the theoretical thermorefractive noise limit by making
the spiral resonator with larger optical mode volume, which can be made possible by longer optical roundtrip length and thicker silica layer. This will improve the fractional frequency stability further. Potentially, silica ridge structure can increase the mode volume per unit silicon chip area an order of magnitude larger and also enable the integration with other chip-based optical components[89]. Combined with emerging microcomb technology[39, 40, 41], our work shows the potential of an optical frequency division system on a chip for the next generation of portable microwave sources.
Chapter 6
Stimulated Brillouin Laser from Optical Microresonator
Stimulated Brillouin scattering (SBS) in high-Q microresonators enables the generation of narrow-linewidth laser and low-phase-noise microwave. The linewidth of the stimulated Brillouin laser(SBL) is known to be Schawlow-Townes-like, limited by the thermal phonon occupancy(nT). In this chapter, we study the nT-limited nature of the SBL linewidth at cryogenic temperatures. Our work confirms the SBL linewidth theory prediction and pro- vides support for the unusual quantum limit of linewidth in these laser systems. In addition, a microresonator SBL-based gyroscope is demonstrated as one of the SBL applications.